I/O embedding and broadcasting in star interconnection networks

The issues of communication between a host or central controller and processors, in large interconnection networks are very important and have been studied in the past by several researchers. There is a plethora of problems that arise when processors are asked to exchange information on parallel computers on which processors are interconnected according to a specific topology. In robust networks, it is desirable at times to send (receive) data/control information to (from) all the processors in minimal time. This type of communication is commonly referred to as broadcasting. To speed up broadcasting in a given network without modifying its topology, certain processors called stations can be specified to act as relay agents. In this thesis, broadcasting issues in a star-based interconnection network are studied. The model adopted assumes all-port communication and wormhole switching mechanism. Initially, the problem treated is one of finding the minimum number of stations required to cover all the nodes in the star graph with i-adjacency. We consider 1-, 2-, and 3-adjacencies and determine the upper bound on the number of stations required to cover the nodes for each case. After deriving the number of stations, two algorithms are designed to broadcast the messages first from the host to stations, and then from stations to remaining nodes; In addition, a Binary-based Algorithm is designed to allow routing in the network by directly working on the binary labels assigned to the star graph. No look-up table is consulted during routing and minimum number of bits are used to represent a node label. At the end, the thesis sheds light on another algorithm for routing using parallel paths in the star network

Topological Properties and Broadcasting Algorithmsof the Generalized-Star Cube

Abstract—In this research, another version of the star cube called the generalized-star cube, GSC(n, k, m), is presented as a three level interconnection topology. GSC(n, k, m) is a product graph of the (n, k)-star graph and the m-dimensional hypercube (m-cube). It can be constructed in one of two ways: to replace each node in an m-cube with an (n, k)-star graph, or to replace each node in an (n, k)-star graph with an m-cube. Because there are three parameters m, n, and k, the network size of GSC(n, k, m) can be changed more flexibly than the star graph, star-cube, and (n, k)-star graph. We first investigate the topological properties of the GSC(n, k, m), such as the node degree, diameter, average distance, and cost. Also, the regularity and node symmetry of the GSC(n, k, m) are derived.Then, we illustrate the broadcasting algorithms for both of the single-port and all-port models. To develop these algorithms, we use the spanning binomial tree, the neighbourhood broadcasting algorithm, and the minimum dominating set. The complexities of the broadcasting algorithms are also examined

Properties and algorithms of the (n, k)-arrangement graphs

The (n, k)-arrangement interconnection topology was first introduced in 1992. The (n, k )-arrangement graph is a class of generalized star graphs. Compared with the well known n-star, the (n, k )-arrangement graph is more flexible in degree and diameter. However, there are few algorithms designed for the (n, k)-arrangement graph up to present. In this thesis, we will focus on finding graph theoretical properties of the (n, k)- arrangement graph and developing parallel algorithms that run on this network. The topological properties of the arrangement graph are first studied. They include the cyclic properties. We then study the problems of communication: broadcasting and routing. Embedding problems are also studied later on. These are very useful to develop efficient algorithms on this network. We then study the (n, k )-arrangement network from the algorithmic point of view. Specifically, we will investigate both fundamental and application algorithms such as prefix sums computation, sorting, merging and basic geometry computation: finding convex hull on the (n, k )-arrangement graph. A literature review of the state-of-the-art in relation to the (n, k)-arrangement network is also provided, as well as some open problems in this area

Fault-free longest paths in star networks with conditional link faults

AbstractThe star network, which belongs to the class of Cayley graphs, is one of the most versatile interconnection networks for parallel and distributed computing. In this paper, adopting the conditional fault model in which each node is assumed to be incident with two or more fault-free links, we show that an n-dimensional star network can tolerate up to 2n−7 link faults, and be strongly (fault-free) Hamiltonian laceable, where n≥4. In other words, we can embed a fault-free linear array of length n!−1 (n!−2) in an n-dimensional star network with up to 2n−7 link faults, if the two end nodes belong to different partite sets (the same partite set). The result is optimal with respect to the number of link faults tolerated. It is already known that under the random fault model, an n-dimensional star network can tolerate up to n−3 faulty links and be strongly Hamiltonian laceable, for n≥3

Reconfiguration for Fault Tolerance and Performance Analysis

Architecture reconfiguration, the ability of a system to alter the active interconnection among modules, has a history of different purposes and strategies. Its purposes develop from the relatively simple desire to formalize procedures that all processes have in common to reconfiguration for the improvement of fault-tolerance, to reconfiguration for performance enhancement, either through the simple maximizing of system use or by sophisticated notions of wedding topology to the specific needs of a given process. Strategies range from straightforward redundancy by means of an identical backup system to intricate structures employing multistage interconnection networks. The present discussion surveys the more important contributions to developments in reconfigurable architecture. The strategy here is in a sense to approach the field from an historical perspective, with the goal of developing a more coherent theory of reconfiguration. First, the Turing and von Neumann machines are discussed from the perspective of system reconfiguration, and it is seen that this early important theoretical work contains little that anticipates reconfiguration. Then some early developments in reconfiguration are analyzed, including the work of Estrin and associates on the fixed plus variable restructurable computer system, the attempt to theorize about configurable computers by Miller and Cocke, and the work of Reddi and Feustel on their restructable computer system. The discussion then focuses on the most sustained systems for fault tolerance and performance enhancement that have been proposed. An attempt will be made to define fault tolerance and to investigate some of the strategies used to achieve it. By investigating four different systems, the Tandern computer, the C.vmp system, the Extra Stage Cube, and the Gamma network, the move from dynamic redundancy to reconfiguration is observed. Then reconfiguration for performance enhancement is discussed. A survey of some proposals is attempted, then the discussion focuses on the most sustained systems that have been proposed: PASM, the DC architecture, the Star local network, and the NYU Ultracomputer. The discussion is organized around a comparison of control, scheduling, communication, and network topology. Finally, comparisons are drawn between fault tolerance and performance enhancement, in order to clarify the notion of reconfiguration and to reveal the common ground of fault tolerance and performance enhancement as well as the areas in which they diverge. An attempt is made in the conclusion to derive from this survey and analysis some observations on the nature of reconfiguration, as well as some remarks on necessary further areas of research

Properties and algorithms of the (n, k)-star graphs

The (n, k)-star interconnection network was proposed in 1995 as an attractive alternative to the n-star topology in parallel computation. The (n, k )-star has significant advantages over the n-star which itself was proposed as an attractive alternative to the popular hypercube. The major advantage of the (n, k )-star network is its scalability, which makes it more flexible than the n-star as an interconnection network. In this thesis, we will focus on finding graph theoretical properties of the (n, k )-star as well as developing parallel algorithms that run on this network. The basic topological properties of the (n, k )-star are first studied. These are useful since they can be used to develop efficient algorithms on this network. We then study the (n, k )-star network from algorithmic point of view. Specifically, we will investigate both fundamental and application algorithms for basic communication, prefix computation, and sorting, etc. A literature review of the state-of-the-art in relation to the (n, k )-star network as well as some open problems in this area are also provided

Properties and algorithms of the hyper-star graph and its related graphs

The hyper-star interconnection network was proposed in 2002 to overcome the drawbacks of the hypercube and its variations concerning the network cost, which is defined by the product of the degree and the diameter. Some properties of the graph such as connectivity, symmetry properties, embedding properties have been studied by other researchers, routing and broadcasting algorithms have also been designed. This thesis studies the hyper-star graph from both the topological and algorithmic point of view. For the topological properties, we try to establish relationships between hyper-star graphs with other known graphs. We also give a formal equation for the surface area of the graph. Another topological property we are interested in is the Hamiltonicity problem of this graph. For the algorithms, we design an all-port broadcasting algorithm and a single-port neighbourhood broadcasting algorithm for the regular form of the hyper-star graphs. These algorithms are both optimal time-wise. Furthermore, we prove that the folded hyper-star, a variation of the hyper-star, to be maixmally fault-tolerant